The Breath of Uncertainty

One of the problems which arises when we mistake a rope for a snake is that it is impossible for us properly to identify the snake. We cannot determine whether it is a Russell's Pit Viper or a Cobra. Not only can we not determine the species of the snake, but if we examine it too closely we'll find hemp fibers at the ends and a three-strand spiral winding. A similar problem shows up in our physics. If, through apparitional causation, we see the underlying reality as a universe in space and time, then, within that universe, there appear certain details which have proved to be beyond the possibility of finding out. The universe is made of hydrogen. The hydrogen is made of electricity. And the electricity takes the form of protons and electrons which hold their distance from each other. Why? We say that the proton is a positive charge and the electron is a negative charge, and we know that the attraction between positive and negative charges is surpassingly great. We may get an idea of the magnitude of that attraction if we consider two grains of sand each one millimeter in diameter and placed about seventy five feet apart. If one of these grains of sand were made entirely of positive charges and the other, entirely of negative charges, then the electrical pull between them would be equivalent to the pull required to pick up one hundred and eight, fifty-thousand-ton battleships strung together as a rosary. Since at half that distance the pull would be four times as great and at a thousandth of that distance it would be a million times as great, we cannot handily overlook the pull, even between a single proton and its electron, at the distance of their proximity in an atom. Yet the electron will not sit down. Why? It is simply because of this breath of uncertainty which necessarily plagues our perception of a universe of mass and energy time. The reason for the uncertainty may be simply illustrated. If three golf balls are placed on the floor near the center of a darkened room, and if several persons, each with a bag of ping pong balls, are seated around the edge of the room, then the people around the edge of the room can discover the positions of the golf balls by rolling their ping pong balls against them in the dark. The ping pong balls, being much lighter than the golf balls, will bounce off the latter without seriously moving them. It would be impossible, however, to discover the positions of ping pong balls by rolling golf balls against them since the impact of the golf balls would destroy the information being sought. The problem of determining the position and momentum of the electron in the hydrogen atom is quite similar. With what shall we bombard it so as to disturb it as little as possible and yet get back the information? Bombarding it with a proton is like rolling a golf ball at a ping pong ball. It's like trying to find out about butterflies with a hatchet. It's too destructive to the butterflies. Even another electron is too massive for our ammunition. And if we turn to radiation the problem is no nearer solution, since the radiation itself comes in discrete packages (photons), and the energy of an ultraviolet photon is enough to knock the electron away from the proton entirely. If we go to photons of lower energy we find that they are associated with longer wavelengths, and, when the wavelengths become long with respect to the distance across an atom, they can no longer carry information about the position of the electron within the atom. It would be like measuring the length of a beetle with an odometer. Heisenberg's famous uncertainty principle is the result of a careful investigation of the limitation thus imposed on the physical measurement of a physical system. Any apparatus which we may set up to allow us to measure accurately the position of a particle makes it impossible for us, simultaneously, to measure accurately its momentum. Likewise, any apparatus which we may set up to allow us to measure accurately the momentum of a particle makes it impossible for us, simultaneously, to measure its position. There is a necessary uncertainty in our measurements such that the product of our uncertainty in the position of a particle and our uncertainty in its momentum can never be less than a certain small amount designated as Planck's Constant, h, over two pi. Now if the electron were to sit on the proton, then the uncertainty in its position would be so small that the necessary uncertainty in its momentum would drive it off. Why? Because we cannot have a large uncertainty about a very small quantity. One could not mistake the weight of a mouse by a pound or a ton. If an electron is sitting on a proton, the uncertainty in its momentum must be so large that the momentum associated with that uncertainty is enough to drive it off. The existence of the hydrogen atom itself, then, depends on this uncertainty. And the uncertainty arises from the necessary interaction between the perceiver and the perceived, or, rather, between the instrument of perception and the object perceived. We know now, from our physics, that the perceiver is always mixed up in what he sees. Every portrait of the universe is signed. Every description of the physical universe is made from the standpoint of some perceiver associated with some instrument of perception. Now the very curious thing about this situation is that the behavior of matter is itself determined by what we can and cannot know. It is a little like the stock market. The behavior of the stock market depends on the ignorance of those who play it. The universe is made of hydrogen, yet the hydrogen atom itself, like any apparition, exists only because of this breath of uncertainty. It can easily be shown that nuclear energy is related to this uncertainty, and that only if our uncertainty in the position of an event in space and time were total could the momentum and the energy associated with that event go to zero. As George Gamow pointed out long ago, it is the increased uncertainty in the position of the charge in a deuteron (one electron on two protons) which allows the uncertainty in the momentum (and, therefore, the momentum associated with that uncertainty) to fall. An electron confined to a single proton will jump away, whereas an electron confined to two will not. The larger the nucleus the larger the uncertainty in position and, therefore, the lower the associated momentum. It is only the disruptive effect of the increased electrical charge that raises the electrical energy (not the nuclear energy) of larger nuclei, rendering them less and less stable beyond iron, and radioactive beyond uranium. If, and only if, our uncertainty in the position of a charge were total could its momentum fall to zero. And only if our uncertainty in the time of an event were total could its energy (the time component of the momentum) fall to zero. If you can know where something is in space and time, you've bought the whole can of worms. To know where something is to know where it is with respect to other things. And to know where something it is to know that it is small enough so that its position could be accurately determined. The only reason that the distances from city to city can be designated on a road map to within a mile is because the measurements are made from city hall to city hall, and the city halls are small with respect to a mile. To know where a proton is is to know its position with respect to all the other matter in the observable universe, and then the undividedness will show through as its gravitational energy. Also, to know where the proton is is to know that it is small, and then the infinitude will show through as its electrical energy. It has already been pointed out that its gravitational and electrical energies are the same thing. They are two sides of one coin. But if they are the two sides, the nuclear energy is the edge of that same coin. They are all the same thing. Energy is apparitional. Only its changes are transformational. To see anything in space and time is to see the universe which we see. The two great changes which have come in our physics since Swamiji's day are relativity theory and quantum mechanics and each is associated with a paradox. Relativity, as we have seen, in its effort to the save the objectivity of the universe, had to throw in the sponge on the separation between the perceiver and the perceived on which the concept of objectivity was based. Here, in quantum mechanics, we see our second paradox. The most certain of our certain knowledge of physics is now stated in terms of quantum mechanics and yet our entire knowledge of quantum mechanics rests on this unavoidable uncertainty.